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The Glyptothek was commissioned by the Crown Prince (later King) Ludwig I of Bavaria alongside other projects, such as the neighboring Königsplatz and the building which houses the State Collection of Greek and Roman Antiquities, as a monument to ancient Greece. He envisioned a "German Athens", in which the ancient Greek culture would be remembered; he had this built in front of the gates of Munich. The Glyptothek is Munich's oldest public museum.

In the few years between 1806 and the opening of the museum in 1830, Ludwig completed a notable collection of Greek and Roman sculpture. Through his agents, he managed to acquire such pieces as the Medusa Rondanini, the Barberini Faun, and, in 1813, the figures from the Aphaea temple on Aegina.

The museum was designed in the Classical Greek - Italian style. The portico is Ionic, and the outer walls contain niches, in which 18 original Roman and Greek sculptures stand, six on each wall (except the back). The thirteen rectangular, square or round rooms are arranged around a courtyard, the vestibule in the central building dominates the halls of height. In front of the vestibule is the portico of twelve Ionic columns. The overlying gable includes a group of Johann Martin von Wagner represents Athena as protector of the plastic arts. The exterior walls are adorned with sculptures in niches, while the windows are open to the interior courtyard. The sculptures represent mythical or historical representatives of the arts, these are in the front of the Königsplatz Daedalus, Prometheus, Hadrian, Pericles, Phidias and Hephaestus. On the western and eastern side of the building there are sculptors of the Renaissance and of the times when the Glyptothek was built, including Bertel Thorvaldsen and Antonio Canova, whose works were once on display earlier in the Hall of the Glyptothek but were later moved to the Neue Pinakothek.

The museum was originally built completely out of marble. However, during World War II the museum was bombed, and later reconstructed. The walls from the interior are composed of red brick and painted with a light plaster. The interior has domed vaulting.

The Glyptothek contains sculptures dating from the archaic age (c. 650 BC) to the Roman era (c. 550 AD). Other notable sculptures, mosaics and reliefs can also be found here.
This collection is complemented by the terracotta and bronze collections in the Staatliche Antikensammlung (State Collection of Greek and Roman Antiquities), which is located opposite the Glyptothek.

Among the most famous sculptures covering Archaic Greece are the Munich Kouros (statue of an adolescent from Attica, c. 540 BC), the Kouros of Tenea (statue of an adolescent from Corinth, c. 560 BC) and the temple figures from Aegina (510-480 BC). Of the latter, there are in fact two sets of similar sculptures at the Glyptothek. As archeologists excavated the site at Aegina, these two sets were discovered, and it was later theorized that the original temple was destroyed during the Peloponnesian War and another temple was erected shortly after in its place. The extant temple of c. 500 BC was built over the remains of an earlier temple of c. 570 BC, which was destroyed by fire c. 510 BC. The elements of this destroyed temple were buried in the infill for the larger, flat terrace of the later temple, and are thus well preserved.

An overview of the room containing the Roman period art with the bust of Emperor Traian (reign 98–117 CE) in the front.

The Glyptothek keeps a large collection of Roman busts, among the most famous ones are the busts of Gaius Marius and Sulla (c. 40 BC), the Emperors Augustus (c. 40 AD), Nero (65 AD), Septimius Severus (200 AD) and his wife Julia Domna (195 AD). A heroised statue portrays Domitian as prince (70/80 AD). With the support of the cultural foundations of the German states, the Glyptothek was able to acquire in 2017 a bust of Caligula (c. 40 AD), excavated in Córdoba in 1937. The Emperor, like the Munich portrait of his ancestor Augustus (Augustus Bevilacqua), bears the corona civica. To the major attractions belong also a colossal statue of Apollo (1st/2nd centuries AD) from a Roman villa in Tuscany, several Roman sarcophagus reliefs and mosaic floors. An imitation of the classical style is the Roman head of a youth in bronze (ca Christ's birth). The Roman period is also represented by several reliefs (Relief of gladiators, 1st century BC) and mosaics (Aion mosaic, c. 200–250 AD).